---
description: "Futures hedging strategy that uses futures contracts to offset price or interest-rate risk on an underlying asset position, with variants for cross-hedging and duration-based interest-rate risk hedging."
tags: [futures, hedging, risk-management, interest-rate, cross-hedge]
---

# Hedging Risk with Futures

**Section**: 10.1 | **Asset Class**: Futures | **Type**: Hedging / Risk Management

## Overview
Futures contracts allow traders to mitigate exposure to price risk on an underlying asset. A trader who anticipates needing to buy (sell) an asset at a future date can lock in a price today by buying (selling) a futures contract. The strategy eliminates directional price exposure at the cost of potentially missing favourable price moves. Variants address situations where no exact futures contract exists (cross-hedging) and interest-rate risk on fixed-income assets.

## Construction / Mechanics
**Basic hedge**: A trader expects to buy (sell) X units of an asset at time T.
- To hedge rising prices: buy futures contracts at time t for delivery at T.
- To hedge falling prices: sell futures contracts at time t for delivery at T.

The futures position offsets the P&L on the underlying physical exposure.

## Return Profile
The hedge eliminates (or substantially reduces) the P&L variability due to the hedged risk factor. The net position approximates a risk-free return when the hedge ratio is well-calibrated. Basis risk (see cross-hedging) is the residual risk that remains.

## Key Parameters / Signals
| Parameter | Description |
|-----------|-------------|
| Hedge ratio | Number of futures contracts per unit of underlying exposure |
| Delivery date T | Futures expiry chosen to match or exceed the hedging horizon |
| Basis risk | Residual risk when futures price and spot price do not move in perfect lockstep |

## Variations

### 10.1.1 Cross-Hedging
When a futures contract for the exact asset to be hedged does not exist, a futures contract on a correlated asset can be used. The payoff at maturity T of the cross-hedged position (short futures, unit hedge ratio) is:

```
S(T) - F(t,T) + F(t,T)
= [S*(T) - F(t,T)] + [S(T) - S*(T)] + F(t,T)                (463)
```

where the subscript * denotes the underlying of the futures contract (different from the hedged asset), S(T) is the spot price of the hedged asset, and F(t,T) is the futures price.

- First term [S*(T) - F(t,T)]: basis risk from the difference between futures price and the futures' underlying spot at delivery.
- Second term [S(T) - S*(T)]: risk from the difference between the two underlying assets.

In practice the optimal hedge ratio h ≠ 1 and can be estimated via serial regression of the hedged asset's spot return on the futures return, or by other methods.

### 10.1.2 Interest Rate Risk Hedging
Fixed-income assets are sensitive to interest rate changes. Futures on interest rate instruments (e.g., T-bond futures) can be used to hedge this risk.

- Long hedge (buy futures): protects against rising asset prices (falling rates)
- Short hedge (sell futures): protects against falling asset prices (rising rates)

P&L for the long hedge established at t=0 with unit hedge ratio and maturity T:
```
P_L(t,T) = B(0,T) - B(t,T)                                   (464)
P_S(t,T) = B(t,T) - B(0,T)                                   (465)
```
where the futures basis is:
```
B(t,T) = S(t) - F(t,T)                                       (466)
```

**Conversion factor model** (for bonds in a futures delivery basket):
```
h_C = C × (M_B / M_F)                                        (467)
```
where M_B is bond notional, M_F is futures notional, C is the conversion factor.

**Modified duration hedge ratio** (applicable to both deliverable and non-deliverable bonds):
```
h_D = β × (D_B / D_F)                                        (468)
```
where D_B is the dollar duration of the bond, D_F is the dollar duration of the futures, and β is the sensitivity of bond yield changes to futures yield changes (often set to 1).

## Notes
- Basis risk is the primary residual risk in any futures hedge; it arises from imperfect correlation between futures and spot prices.
- The conversion factor model applies only to T-bond and T-note futures; the duration model is more general.
- β in Eq. (468) can be estimated from historical regression of bond yield changes on futures yield changes.
- Cross-hedges with dissimilar underlying assets carry additional residual risk that simple regression-based hedge ratios may not fully capture.
- Hedging eliminates upside as well as downside; traders should consider whether they need a full hedge or a partial one.